Entropies, Volumes, and Einstein Metrics
Identifieur interne : 000196 ( Main/Merge ); précédent : 000195; suivant : 000197Entropies, Volumes, and Einstein Metrics
Auteurs : D. Kotschick [Allemagne]Source :
- Springer Proceedings in Mathematics [ 2190-5614 ] ; 2012.
Abstract
Abstract: We survey the definitions and some important properties of several asymptotic invariants of smooth manifolds, and discuss some open questions related to them. We prove that the (non-)vanishing of the minimal volume is a differentiable property, which is not invariant under homeomorphisms. We also formulate an obstruction to the existence of Einstein metrics on four-manifolds involving the volume entropy. This generalizes both the Gromov–Hitchin–Thorpe inequality proved in [Kotschick, On the Gromov–Hitchin–Thorpe inequality, C. R. Acad. Sci. Paris 326 (1998), 727–731], and Sambusetti’s obstruction [Sambusetti, An obstruction to the existence of Einstein metrics on 4-manifolds, Math. Ann. 311 (1998), 533–547].
Url:
DOI: 10.1007/978-3-642-22842-1_2
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